Stat 210 Exam Two ___________________________________
Read these directions carefully. Take your time and check your work. Many students do not take enough time on their
tests. Each problem is worth four points. You may choose exactly question to omit by writting ʺomitʺ in the answer blank.
If you do not omit any, or omit more than one, all will be graded.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the events are disjoint.
1) Get stung by a bee.
Get stung by a wasp.
A) Yes
1)
B) No
C) Both yes and no
Is Event B dependent or independent of Event A?
2) A: A mosquito lands on your arm.
B: You get a mosquito bite.
A) Dependent
B) Independent
2)
C) Rebublican
D) Democrat
Find the indicated probability.
3) Find the probability of correctly answering the first 3 questions on a multiple choice test if random
guesses are made and each question has 6 possible answers.
1
1
1
C)
D)
A) 2
B)
216
729
2
4) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy Nonsmoker smoker smoker Total
Men
390
34
42
466
Women
446
35
44
525
Total
836
69
86
991
3)
4)
If two different people are randomly selected from the 991 subjects, find the probability that they
are both heavy smokers. Round to six decimal places.
A) 0.001796
B) 0.007451
C) 0.007531
D) 0.0001352
Find the indicated probability. Round to the nearest thousandth.
5) A sample of 4 different calculators is randomly selected from a group containing 18 that are
defective and 40 that have no defects. What is the probability that at least one of the calculators is
defective?
A) 0.215
B) 0.774
C) 0.180
D) 0.785
1
5)
Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.
6) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
6)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years
of age.
2
1
3
1
B)
C)
D)
A)
5
3
5
2
Evaluate the expression.
7) 10C3
A) 3
7)
B) 5040
C) 120
D) 240
Solve the problem.
8) How many ways can an IRS auditor select 3 of 9 tax returns for an audit?
A) 729
B) 84
C) 6
8)
D) 504
9) A pollster wants to minimize the effect the order of the questions has on a personʹs response to a
survey. How many different surveys are required to cover all possible arrangements if there are 11
questions on the survey?
A) 11
B) 121
C) 3,628,800
D) 39,916,800
Identify the given random variable as being discrete or continuous.
10) The exact braking time of a car
A) Discrete
B) Continuous
9)
10)
C) Public
Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
11)
11)
x P(x)
0 0.07
1 0.15
2 0.20
3 0.41
4 0.17
A) Probability distribution.
B) Not prob. dist.; does not add to one
C) Not prob. dist.; probabilities greater than one
D) Not prob. dist.; probabilities less than zero
2
Find the mean of the given probability distribution.
12) In a certain town, 30% of adults have a college degree. The accompanying table describes the
probability distribution for the number of adults (among 4 randomly selected adults) who have a
college degree.
x P(x)
0 0.2401
1 0.4116
2 0.2646
3 0.0756
4 0.0081
A) μ = 1.10
B) μ = 1.44
C) μ = 1.20
D) μ = 2.00
Provide an appropriate response. Round to the nearest hundredth.
13) Find the standard deviation for the given probability distribution.
x P(x)
0 0.37
1 0.13
2 0.06
3 0.15
4 0.29
A) σ = 1.81
B) σ = 2.90
C) σ = 1.70
12)
13)
D) σ = 2.52
Answer the question.
14) Focus groups of 15 people are randomly selected to discuss products of the Yummy Company. It
is determined that the mean number (per group) who recognize the Yummy brand name is 12.5,
and the standard deviation is 0.58. Would it be unusual to randomly select 15 people and find
that fewer than 9 recognize the Yummy brand name?
A) Yes
B) No
C) 42
D) Purple
14)
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The
probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table.
Probabilities of Girls
x(girls) P(x) x(girls) P(x) x(girls) P(x)
0
0.000
5
0.122
10
0.061
1
0.001
6
0.183
11
0.022
2
0.006
7
0.209
12
0.006
3
0.022
8
0.183
13
0.001
4
0.061
9
0.122
14
0.000
15) Find the probability of selecting 9 or more girls.
A) 0.061
B) 0.212
15)
C) 0.001
3
D) 0.122
Provide an appropriate response.
16) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning
ticket is to be $500. What is your expected value?
A) -$1.00
B) $0.00
C) -$0.40
D) -$0.50
Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
17) Choosing 4 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time
without replacement, keeping track of the number of red marbles chosen.
A) Not binomial: the trials are not independent.
B) Procedure results in a binomial distribution.
C) Not binomial: there are too many trials.
D) Not binomial: there are more than two outcomes for each trial.
16)
17)
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability
formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal
places.
18) n = 5, x = 2, p = 0.70
18)
A) 0.700
B) 0.198
C) 0.132
D) 0.464
Find the indicated probability. Round to three decimal places.
19) Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally
likely and that the births are independent events.
A) 0.234
B) 0.656
C) 0.891
D) 0.109
Find the indicated probability.
20) In a survey of 300 college graduates, 56% reported that they entered a profession closely related to
their college major. If 8 of those survey subjects are randomly selected without replacement for a
follow-up survey, what is the probability that 3 of them entered a profession closely related to
their college major?
A) 0.0637
B) 0.176
C) 0.838
D) 0.162
Solve the problem.
21) On a multiple choice test with 17 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 8.5
B) 5.7
C) 12.8
D) 4.3
22) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 15.
Find the standard deviation for the number of seeds germinating in each batch.
A) 9.9
B) 1.8
C) 3.2
D) 31.5
4
19)
20)
21)
22)
Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard
deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ.
23)
23) According to AccuData Media Research, 36% of televisions within the Chicago city limits are
tuned to ʺEyewitness Newsʺ at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500
such televisions are randomly selected and checked to determine what is being watched. Would it
be unusual to find that 919 of the 2500 televisions are tuned to ʺEyewitness Newsʺ?
A) Yes
B) No
C) 42
D) Purple
Use the Poisson Distribution to find the indicated probability.
24) A mountain search and rescue team receives a mean of 0.78 calls per day. Find the probability that
on a randomly selected day, they will receive fewer than two calls.
A) 0.1840
B) 0.1394
C) 0.8160
D) 0.3576
25) The number of calls received by a car towing service averages 19.2 per day (per 24-hour period).
After finding the mean number of calls per hour, find the probability that in a randomly selected
hour the number of calls is 2.
A) 0.17973
B) 0.11503
C) 0.15816
D) 0.14379
5
24)
25)
Answer Key
Testname: 2016 FALL TEST 2
1) B
2) A
3) C
4) B
5) D
6) C
7) C
8) B
9) D
10) B
11) A
12) C
13) C
14) A
15) B
16) D
17) A
18) C
19) C
20) D
21) D
22) B
23) B
24) C
25) D
6